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Keywords = Hertzian pressure

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15 pages, 3096 KiB  
Article
An Experimental Study on the Impact of Roughness Orientation on the Friction Coefficient in EHL Contact
by Matthieu Cordier, Yasser Diab, Jérôme Cavoret, Fida Majdoub, Christophe Changenet and Fabrice Ville
Lubricants 2025, 13(8), 340; https://doi.org/10.3390/lubricants13080340 - 31 Jul 2025
Viewed by 291
Abstract
Optimising the friction coefficient helps reduce friction losses and improve the efficiency of mechanical systems. The purpose of this study is to experimentally investigate the impact of roughness orientation on the friction coefficient in elastohydrodynamic (EHD) contact. Tests were carried out on a [...] Read more.
Optimising the friction coefficient helps reduce friction losses and improve the efficiency of mechanical systems. The purpose of this study is to experimentally investigate the impact of roughness orientation on the friction coefficient in elastohydrodynamic (EHD) contact. Tests were carried out on a twin-disc machine. Three pairs of discs of identical material (nitrided steel) and geometry were tested: a smooth pair (the root mean square surface roughness Sq = 0.07 µm), a pair with transverse roughness and another with longitudinal roughness. The two rough pairs have similar roughness amplitudes (Sq = 0.5 µm). A comparison of the friction generated by these different pairs was carried out to highlight the effect of the roughness orientation under different operating conditions (oil injection temperature from 60 to 80 °C, Hertzian pressure from 1.2 to 1.5 GPa and mean rolling speed from 5 to 30 m/s). Throughout all the tests conducted in this study, longitudinal roughness resulted in higher friction than transverse, with an increase of up to 30%. Moreover, longitudinal roughness is more sensitive to variations in operating conditions. Finally, in all tests, the asperities of longitudinal roughness were found to influence the friction behaviour, unlike transverse roughness. Full article
(This article belongs to the Special Issue Experimental Modelling of Tribosystems)
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27 pages, 4262 KiB  
Article
Concave Contact Geometry for Enhanced Sealing and Structural Integrity in Ultra-High Pressure Hydrogen Solenoid Valves
by Jaeseong Choi and Hwayoung Kim
Appl. Sci. 2025, 15(11), 6184; https://doi.org/10.3390/app15116184 - 30 May 2025
Viewed by 471
Abstract
Ultra-high-pressure hydrogen solenoid valves face a fundamental design challenge of operating across a wide pressure range from 2 MPa to 87.5 MPa. To address the conflicting requirements of effective sealing at low pressures and structural integrity at high pressures, this study proposes a [...] Read more.
Ultra-high-pressure hydrogen solenoid valves face a fundamental design challenge of operating across a wide pressure range from 2 MPa to 87.5 MPa. To address the conflicting requirements of effective sealing at low pressures and structural integrity at high pressures, this study proposes a novel concave contact geometry based on Hertzian contact theory. Finite element analysis examines the mechanical relationships between plunger curvature radius (R), seat curvature radius (Rₛ), and eccentricity (e). Optimization utilizing Latin hypercube sampling and kriging metamodeling yields an optimal design (Rₚ = 5.73 mm, Rₛ = 4.68 mm, e = 0.95 mm) with an Rₚ/Rₛ ratio of 1.22. The optimized concave contact geometry achieves 23.7% higher contact pressure at 2.0 MPa and 42.7% lower maximum equivalent stress at 87.5 MPa compared to conventional rectangular geometry. Experimental validation confirms the concave contact geometry seals at 1.7 ± 0.2 MPa, below the AIS-195 standard requirement of 2.0 MPa and 69.6% lower than the rectangular design (5.6 ± 0.7 MPa). Structural analysis after 87.5 MPa high-pressure exposure reveals no measurable deformation in the concave design, while the rectangular design exhibits permanent deformation of 0.0580 ± 0.007 mm. This integrated methodology provides a framework for optimizing contact geometries in fluid control components operating under extreme pressure conditions, successfully reconciling contradictory requirements across the entire pressure range. Full article
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22 pages, 5174 KiB  
Article
In Situ Measurement and Mapping of Lubricant Film Temperature in Cylindrical Roller Thrust Bearings Using Thin-Film Sensors
by Manjunath Manjunath, Patrick De Baets and Dieter Fauconnier
Machines 2025, 13(4), 297; https://doi.org/10.3390/machines13040297 - 2 Apr 2025
Cited by 1 | Viewed by 400
Abstract
This study explores the in situ measurement of contact temperature in thermo-elastohydrodynamic lubrication (TEHL) within cylindrical roller thrust bearings (CRTBs) utilizing vapour-deposited resistive thin-film sensors. The sensors, optimized for compactness and high spatial resolution, were strategically embedded on the stationary bearing raceways near [...] Read more.
This study explores the in situ measurement of contact temperature in thermo-elastohydrodynamic lubrication (TEHL) within cylindrical roller thrust bearings (CRTBs) utilizing vapour-deposited resistive thin-film sensors. The sensors, optimized for compactness and high spatial resolution, were strategically embedded on the stationary bearing raceways near the outer, inner, and mean radius. This configuration enabled a precise measurement of temperature variations in both pure rolling and rolling–sliding regions of the CRTBs. The experimental results revealed a consistent decrease in temperature from the inner and outer radius zones towards the mean radius as the slip-to-roll ratio (SRR) decreased in these regions. Temperature profiles showed an early rise in the inlet zone attributed to thermal inlet shear. At higher speeds, a secondary temperature peak indicative of full-film lubrication was observed in the outlet zone immediately following the Hertzian contact. The study further shows the influence of surface pressure, shear rates, sliding friction, and circumferential speed on contact temperature dynamics, offering insights into their complex interplay. Additionally, viscosity variations due to different oil temperatures were found to critically affect the rate of temperature rise and the propensity for mixed friction phenomena. A higher viscosity resulted in an earlier onset of the temperature rise in the contact, while a lower viscosity and higher speeds promote mixed lubrication, leading to reduced contact film temperatures. These findings provide valuable insights into the behaviour of CRTB-lubricated contacts under various operating conditions and serve as crucial validation data for advanced TEHL computational models. Full article
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30 pages, 11075 KiB  
Article
The Elasto-Plastic Contact Models of Cylinder-Based and Sphere-Based Fractal Rough Surfaces
by Xiaohui Yang, Bo Bai and Shimin Mao
Appl. Sci. 2025, 15(4), 1994; https://doi.org/10.3390/app15041994 - 14 Feb 2025
Viewed by 729
Abstract
The elasto-plastic contact models of cylinder-based and sphere-based fractal rough surfaces are developed. In the two models, the critical contact areas of a single asperity are scale-dependent. With an increase in the contact load and contact area, a transition from elastic, elasto-plastic to [...] Read more.
The elasto-plastic contact models of cylinder-based and sphere-based fractal rough surfaces are developed. In the two models, the critical contact areas of a single asperity are scale-dependent. With an increase in the contact load and contact area, a transition from elastic, elasto-plastic to full plastic deformation takes place in this order. The truncated asperity size distribution functions of different frequency indexes in different contact zones are deduced. The relations between the total real contact area and total contact load for cylinder-based and sphere-based fractal rough surfaces are obtained. The pressure distributions in the contact zone are obtained. The results of elasto-plastic contact models show that the mechanical property of cylinder-based and sphere-based fractal rough surfaces depends on the range of the frequency index of asperities. When the first six frequency indexes are smaller than the elastic critical frequency index, the cylinder-based and sphere-based fractal rough surfaces approximately appear to have an elastic property in the complete contact process. When the minimum frequency index is greater than the elastic critical frequency index, elastic deformation first takes place in the rough surfaces. Then, elasto-plastic deformation takes place with an increase in the total contact load. In elastic deformation, the ratios of the peak pressures of present fractal models to those of Hertzian models are constant for a given range of frequency indexes. In inelastic deformation, the ratios of the peak pressures are inversely proportional to the total contact load. Full article
(This article belongs to the Special Issue Research on Friction and Lubrication: Surfaces, Bearings and Gears)
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14 pages, 9275 KiB  
Article
Effect of Graphene Nanoplatelets as Lubricant Additive on Fuel Consumption During Vehicle Emission Tests
by Eduardo Tomanik, Wania Christinelli, Pamela Sierra Garcia, Scott Rajala, Jesuel Crepaldi, Davi Franzosi, Roberto Martins Souza and Fernando Fusco Rovai
Eng 2025, 6(1), 18; https://doi.org/10.3390/eng6010018 - 16 Jan 2025
Cited by 1 | Viewed by 1955
Abstract
Lubricant friction modifier additives are used on lower viscosity engine oils to mitigate boundary friction. This work presents the development of a graphene-based material as an oil friction modifier additive, from formulation to actual vehicle tests. The graphene material was initially characterized using [...] Read more.
Lubricant friction modifier additives are used on lower viscosity engine oils to mitigate boundary friction. This work presents the development of a graphene-based material as an oil friction modifier additive, from formulation to actual vehicle tests. The graphene material was initially characterized using scanning electron microscopy (SEM) and Raman spectroscopy, which revealed the predominance of graphene nanoplatelets (GNPs) with an average of nine layers. After functionalization, two GNP additive variants were initially mixed with a fully formulated SAE 0W-20 engine oil and tribologically evaluated using reciprocating sliding tests at 40 and 120 °C and Hertzian pressure up to 1.2 GPa when both variants presented friction reduction. Then, the GNP additive variant with better performance was evaluated in a vehicle emission test using a fully formulated 5W-20 SAE oil as a reference. The addition of 0.1% of GNPs reduced fuel consumption by 2.6% in urban conditions and 0.8% in highway ones. The urban test cycle was FTP75 and higher benefits of the GNP additive occurred especially on the test start, when the engine and oil were still cold and on test portions where the vehicle speed was lower. Full article
(This article belongs to the Special Issue Feature Papers in Eng 2024)
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21 pages, 4673 KiB  
Article
Study on the Damage Characteristics of Wheat Kernels under Continuous Compression Conditions
by Xiaopeng Liu, Ziang Shi, Yonglin Zhang, Hui Li, Jin Zhou and Hongjun Yang
Foods 2024, 13(18), 2981; https://doi.org/10.3390/foods13182981 - 20 Sep 2024
Viewed by 809
Abstract
Peeling wheat yields higher-quality flour. During processing in a flaking machine, wheat kernels undergo continuous compression within the machine’s chamber. As this compression persists, damage to the kernels intensifies and accumulates, eventually leading to kernel breakage. To study the damage characteristics of wheat [...] Read more.
Peeling wheat yields higher-quality flour. During processing in a flaking machine, wheat kernels undergo continuous compression within the machine’s chamber. As this compression persists, damage to the kernels intensifies and accumulates, eventually leading to kernel breakage. To study the damage characteristics of wheat kernels during peeling, this study established a continuous damage model based on Hertzian contact theory and continuous damage theory. The model’s accuracy was validated through experiments, culminating in the calculation of critical parameters for wheat peeling. This study focused on different wheat varieties (Ningmai 22 and Jichun 1) and kernel sizes (the thicknesses of the small, medium, and large kernels were standardized as follows: Ningmai 22—2.67 ± 0.07 mm, 2.81 ± 0.07 mm, and 2.95 ± 0.07 mm; Jichun 1—2.98 ± 0.11 mm, 3.20 ± 0.11 mm, and 3.42 ± 0.11 mm). Continuous compression tests were conducted using a mass spectrometer, and critical damage parameters were analyzed and calculated by integrating the theoretical model with experimental data. The test results showed that the average maximum crushing force (Fc) for small, medium, and large-sized kernels of Ningmai 22 was 96.71 ± 2.27 N, 110.17 ± 2.68 N, and 128.41 ± 2.85 N, respectively. The average maximum crushing deformation (αc) was 0.65 ± 0.08 mm, 0.68 ± 0.13 mm, and 0.77 ± 0.17 mm, respectively. The average elastic–plastic critical pressure (Fs) was 50.21 N, 60.13 N, and 59.08 N, respectively, and the average critical values of elastic–plastic deformation (αs) were 0.37 mm, 0.38 mm, and 0.39 mm, respectively. For Jichun 1, the average maximum crushing force (Fc) for small-, medium-, and large-sized kernels was 113.34 ± 3.15 N, 125.28 ± 3.64 N, and 136.15 ± 3.29 N, respectively. The average maximum crushing deformation (αc) was 0.75 ± 0.11 mm, 0.83 ± 0.15 mm, and 0.88 ± 0.18 mm, respectively. The average elastic–plastic critical pressure (Fs) was 58.11 N, 64.17 N, and 85.05 N, respectively, and the average critical values of elastic–plastic deformation (αs) were 0.45 mm, 0.47 mm, and 0.52 mm, respectively. The test results indicated that during mechanical compression, if the deformation is less than αs, the continued application of the compression load will not result in kernel crushing. However, if the deformation exceeds αs, continued compression will lead to kernel crushing, with the required number of compressions decreasing as the deformation increases. If the deformation surpasses αc, a single compression load is sufficient to cause kernel crushing. Since smaller wheat kernels are more susceptible to breakage during processing, the peeling pressure (F) within the chamber should be controlled to remain below the average elastic–plastic critical pressure (Fs) of small-sized wheat kernels. Additionally, the kernel deformation (α) induced by the flow rate and loading in the chamber should be kept below the average elastic–plastic critical deformation (αs) of small-sized wheat kernels. This paper provides a theoretical foundation for the structural design and optimization of processing parameters for wheat peeling machines. Full article
(This article belongs to the Section Grain)
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16 pages, 3996 KiB  
Article
Elastic and Elastoplastic Contact Mechanics of Concentrated Coated Contacts
by Patricia M. Johns-Rahnejat, Nader Dolatabadi and Homer Rahnejat
Lubricants 2024, 12(5), 162; https://doi.org/10.3390/lubricants12050162 - 7 May 2024
Cited by 4 | Viewed by 2885
Abstract
Machines operate under increasingly harsher contact conditions, causing significant wear and contact fatigue. Sub-surface stresses are responsible for the premature contact fatigue of rolling element bearings, meshing gears, and cam–follower pairs. Surface protection measures include hard, wear-resistant coatings. Traditionally, contact integrity has been [...] Read more.
Machines operate under increasingly harsher contact conditions, causing significant wear and contact fatigue. Sub-surface stresses are responsible for the premature contact fatigue of rolling element bearings, meshing gears, and cam–follower pairs. Surface protection measures include hard, wear-resistant coatings. Traditionally, contact integrity has been predicted using classical Hertzian contact mechanics. However, the theory is only applicable when the contact between a pair of ellipsoidal solids of revolution may be considered as a rigid indenter penetrating a semi-infinite elastic half-space. Many coatings act as thin bonded elastic layers that undergo considerably higher pressures than those predicted by the classical theory. Furthermore, inelastic deformation of bonded solids can cause plastic flow, work-hardening, and elastoplastic behaviour. This paper presents a comprehensive, integrated contact mechanics analysis that includes induced sub-surface stresses in concentrated counterformal finite line contacts for all the aforementioned cases. Generated pressures and deformation are predicted for hard coated surfaces, for which there is a dearth of relevant analysis. The contact characteristics, which are of particular practical significance, of many hard, wear-resistant advanced coatings are also studied. The paper clearly demonstrates the importance of using efficient semi-analytical, detailed holistic contact mechanics rather than the classical idealised methods or empirical numerical ones such as FEA. The novel approach presented for the finite line contact of thin-layered bonded solids has not hitherto been reported in the open literature. Full article
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15 pages, 1013 KiB  
Article
On Boussinesq’s Problem for a Power-Law Graded Elastic Half-Space on Elliptical and General Contact Domains
by Emanuel Willert
Materials 2023, 16(12), 4364; https://doi.org/10.3390/ma16124364 - 13 Jun 2023
Cited by 4 | Viewed by 1405
Abstract
The indentation of a power-law graded elastic half-space by a rigid counter body is considered in the framework of linear elasticity. Poisson’s ratio is assumed to be constant over the half-space. For indenters with an ellipsoidal power-law shape, an exact contact solution is [...] Read more.
The indentation of a power-law graded elastic half-space by a rigid counter body is considered in the framework of linear elasticity. Poisson’s ratio is assumed to be constant over the half-space. For indenters with an ellipsoidal power-law shape, an exact contact solution is derived, based on the generalizations of Galin’s theorem and Barber’s extremal principle for the inhomogeneous half-space. As a special case, the elliptical Hertzian contact is revisited. Generally, elastic grading with a positive grading exponent reduces the contact eccentricity. Fabrikant’s approximation for the pressure distribution under a flat punch of arbitrary planform is generalized for power-law graded elastic media and compared with rigorous numerical calculations based on the boundary element method (BEM). Very good agreement between the analytical asymptotic solution and the numerical simulation is obtained for the contact stiffness and the contact pressure distribution. A recently published approximate analytic solution for the indentation of a homogeneous half-space by a counter body, whose shape slightly deviates from axial symmetry but is otherwise arbitrary, is generalized for the power-law graded half-space. The approximate procedure for the elliptical Hertzian contact exhibits the same asymptotic behavior as the exact solution. The approximate analytic solution for the indentation by a pyramid with square planform is in very good agreement with a BEM-based numerical solution of the same problem. Full article
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14 pages, 5918 KiB  
Article
Determination of the Pressure Dependence of Raman Mode for an Alumina–Glass Pair in Hertzian Contact
by Karl Delbé, Cyril De Sousa, François Grizet, Jean-Yves Paris and Malik Yahiaoui
Materials 2022, 15(23), 8645; https://doi.org/10.3390/ma15238645 - 4 Dec 2022
Cited by 4 | Viewed by 2950
Abstract
Optimising the performance of materials requires, among other things, the characterisation of residual stresses during the design stage. Raman spectroscopy offers access to these residual stresses at the micrometre scale when this inelastic light scattering is active in these materials. In this case, [...] Read more.
Optimising the performance of materials requires, among other things, the characterisation of residual stresses during the design stage. Raman spectroscopy offers access to these residual stresses at the micrometre scale when this inelastic light scattering is active in these materials. In this case, the relationship between the Raman mode shift and the pressure must be known. High-pressure cells with diamond anvils or bending instruments coupled to Raman spectrometers are habitually used to determine this relationship. In this article, we propose a new method that involves a Hertzian contact to obtain this relationship. A device that compresses an alumina ball against a transparent glass plane is connected to a Raman spectrometer. Under these conditions, the contact pressure can be as high as 1.5 GPa. The contact between the glass plane and the ball is observed through a diaphragm. Several hundred Raman spectra are recorded depending on the contact diameter. The spectral profiles obtained represent the shift in the Raman modes of alumina and glass along the contact diameter. Hertz’s theory accurately describes the pressure profile as a function of position for elastic materials. Therefore, the contact diameter can be measured by fitting the spectral profile with a function identical to the Hertz profile. We then deduce the maximum pressure. Next, the calculated pressure profile along the contact diameter is correlated with the spectral profile. We obtain a pressure dependence of the Raman mode with a coefficient equal to 2.07 cm1/GPa for the Eg modes of alumina at 417 cm1, which is in good agreement with the literature. In the case of glass, we refine the measurement of the Q3 mode shift at 1096 cm1 in the studied pressure range compared to the literature. We find a coefficient of 4.31 cm1/GPa. This work on static contacts opens up promising prospects for investigations into dynamic contacts in tribology. Full article
(This article belongs to the Section Advanced Materials Characterization)
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19 pages, 9016 KiB  
Article
Comparative Study of Friction and Wear Performance of PEK, PEEK and PEKK Binders in Tribological Coatings
by Judith M. Pedroso, Marco Enger, Pedro Bandeira and Fernão D. Magalhães
Polymers 2022, 14(19), 4008; https://doi.org/10.3390/polym14194008 - 25 Sep 2022
Cited by 23 | Viewed by 4650
Abstract
Tribological coatings are widely used in industry, particularly when the conventional oil lubrication of sliding surfaces has to be replaced by maintenance-free contacts. This work studies the tribological performance of waterborne tribological coatings based on three binders of the polyaryletherketone (PAEK) family: polyetherketone [...] Read more.
Tribological coatings are widely used in industry, particularly when the conventional oil lubrication of sliding surfaces has to be replaced by maintenance-free contacts. This work studies the tribological performance of waterborne tribological coatings based on three binders of the polyaryletherketone (PAEK) family: polyetherketone (PEK), PEEK, and polyetherketoneketone (PEKK). Even though PEEK is a well-known commercial solution for this type of tribological coatings, PEK and PEKK have never been studied in such a context. PTFE particles were added to all coatings as a solid lubricant. High thermal resistance of the binder materials was confirmed, with decomposition starting above 550 °C, under either N2 or O2 atmosphere. XRD analysis showed that PEK and PEEK are semi-crystalline after being subjected to the coating curing conditions, while PEKK is amorphous. The coatings were successfully applied with thicknesses of 20–30 µm. Tribological measurements showed that the PEK-based coating possesses a coefficient of friction (COF) of 0.08 under high load and pressure conditions (hertzian point contact), which is lower than the reference PEEK-based coating (around 0.11). The PEKK-based coating showed an impressive wear resistance with almost no wear measured compared to the 105 µm wear obtained for PEEK-based coating, while showing a similar COF. These results suggest that PEK and PEKK seem to be interesting alternatives to PEEK and should be further studied for use in tribological coatings. Full article
(This article belongs to the Section Polymer Membranes and Films)
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17 pages, 5573 KiB  
Article
The Applicability of the Hertzian Formulas to Point Contacts of Spheres and Spherical Caps
by Enrico Ciulli, Alberto Betti and Paola Forte
Lubricants 2022, 10(10), 233; https://doi.org/10.3390/lubricants10100233 - 23 Sep 2022
Cited by 22 | Viewed by 6124
Abstract
Hertzian formulas are commonly used for the evaluation of deformation and pressure distribution of non-conformal and slightly conformal mechanical pairs to estimate component stiffness and durability. For the sake of simplicity, their use is extended even to those cases in which Hertz’s hypotheses [...] Read more.
Hertzian formulas are commonly used for the evaluation of deformation and pressure distribution of non-conformal and slightly conformal mechanical pairs to estimate component stiffness and durability. For the sake of simplicity, their use is extended even to those cases in which Hertz’s hypotheses do not hold. This paper summarizes Hertz’s theory and compares the results obtained with theoretical and finite element analysis of the point contact of non-conformal and conformal pairs made of spheres, caps, and spherical seats. This study was motivated by the non-Hertzian behavior of a tilting pad bearing ball-and-socket pivot conforming contact observed by the authors in previous experiments. In particular, the displacement and force relation were investigated by varying the geometrical parameters, the materials, the boundary conditions, and the friction coefficient. In the case of non-conformal contact, the parameter variations had negligible effect in agreement with Hertz’s theory while for conformal contact, the cap and seat height and width and the relative clearance were the most influential parameters on the non-Hertzian behavior. These novel results indicate that in conformal pairs, such as for tilting pad bearing ball-and-socket pivots, whenever Hertz’s hypotheses are not satisfied and the assessment of contact stiffness is crucial, Hertzian formulas should not be applied as done in common practice, instead more accurate numerical or experimental evaluation should be made. Full article
(This article belongs to the Special Issue Special Issue in Elastohydrodynamics: Remembering Ramsey Gohar)
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16 pages, 3716 KiB  
Article
Stick-Slip Phenomena and Acoustic Emission in the Hertzian Linear Contact
by Laura Mariana Babici, Andrei Tudor and Jordi Romeu
Appl. Sci. 2022, 12(19), 9527; https://doi.org/10.3390/app12199527 - 22 Sep 2022
Cited by 12 | Viewed by 3460
Abstract
AE detection and analysis usually requires a specific, costly platform due to its particular burst nature and high-frequency content. This experimental study investigates the relationship between low-demand acoustic emission parameters (AE) and the occurrence of stick–slip (SS) at the Hertzian linear contact. Hence, [...] Read more.
AE detection and analysis usually requires a specific, costly platform due to its particular burst nature and high-frequency content. This experimental study investigates the relationship between low-demand acoustic emission parameters (AE) and the occurrence of stick–slip (SS) at the Hertzian linear contact. Hence, the correlation of basic AE characteristics (amplitude, energy, and evolution in time) with stick–slip characteristics (static and kinetic friction coefficients, amplitude, energy, and evolution in time) is pursued. Tribological tests were conducted on cylinder–plane specimens under dry friction conditions with different loads at different low driving speeds and Hertzian contact pressures at a constant stiffness. The AE, normal, and friction forces were recorded simultaneously on the experimental stand. At the cylinder–plane interface, the jumps specific to the stick–slip phenomenon (friction coefficient—COF) were followed after a few milliseconds by AE jump peaks. The results of the experiments show that the amplitude and energy generated by AE were sensitive to the occurrence of the stick–slip phenomenon, while the AE and COF energies in the stick and slip phases had the same law of variation based on the driving velocities. The results show that the amplitude and energy of the sampled low-frequency AE signals were enough to detect the friction in SS and demonstrate the potential of AE as a tool for detecting and monitoring the tribological behaviour of SS at the linear Hertzian contact. Full article
(This article belongs to the Section Mechanical Engineering)
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21 pages, 3831 KiB  
Article
Non-Newtonian Thermo-Elastohydrodynamics and Sub-Surface Stress Field of High-Performance Racing Spur Gears
by Gajarajan Sivayogan, Nader Dolatabadi, Patricia Johns-Rahnejat, Ramin Rahmani and Homer Rahnejat
Lubricants 2022, 10(7), 146; https://doi.org/10.3390/lubricants10070146 - 8 Jul 2022
Cited by 16 | Viewed by 2686
Abstract
Meshing teeth pairs of involute spur gears often form the final drive of high-performance motorsport transmissions. They are subject to high normal and shear loading. Under transient conditions pertaining to a meshing cycle, the contact conditions alter from the onset of teeth pair [...] Read more.
Meshing teeth pairs of involute spur gears often form the final drive of high-performance motorsport transmissions. They are subject to high normal and shear loading. Under transient conditions pertaining to a meshing cycle, the contact conditions alter from the onset of teeth pair engagement through to maximum normal loading, followed by contact separation. Sliding motion only ceases instantaneously at the pitch point. The regime of lubrication remains mostly in non-Newtonian thermo-elastohydrodynamic conditions. The results show that a starved inlet boundary is attained throughout most of the meshing cycle which leads to the diminution of the pressure spike at the exit from the contact conjunction. The reversing sub-surface shear stresses are the main source of the onset of any inelastic deformation, which is dominated by the primary pressure peak in compliance with the Hertzian maximum pressure. The shear stress field is supplemented by an induced field due to the presence of the pressure spike. Under starved conditions this secondary stress field is diminished. The combined solution of elastohydrodynamics with a thermal network model, non-Newtonian lubricant traction, and sub-surface stress evaluation provides for a comprehensive solution not hitherto reported in the literature. Full article
(This article belongs to the Special Issue Special Issue in Elastohydrodynamics: Remembering Ramsey Gohar)
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18 pages, 2215 KiB  
Article
Edge Pressures Obtained Using FEM and Half-Space: A Study of Truncated Contact Ellipses
by Michael Juettner, Marcel Bartz, Stephan Tremmel, Martin Correns and Sandro Wartzack
Lubricants 2022, 10(6), 107; https://doi.org/10.3390/lubricants10060107 - 1 Jun 2022
Cited by 5 | Viewed by 2881
Abstract
In rolling or gear contacts, truncation of the contact ellipse can occur, for example, when an undercut extends into the contact area. For an elastic calculation approach, the edge constitutes a mathematical singularity, which is revealed by a theoretically infinitely high pressure peak. [...] Read more.
In rolling or gear contacts, truncation of the contact ellipse can occur, for example, when an undercut extends into the contact area. For an elastic calculation approach, the edge constitutes a mathematical singularity, which is revealed by a theoretically infinitely high pressure peak. However, when elastic–plastic material behavior is taken into account, the pressure peak is limited by local hardening and yielding of the material, leading to plastic deformations. As a result, those calculations are rather challenging and the results partly unexpected due to the discontinuity contained in the geometry. Nevertheless, to the authors’ knowledge, hardly any published studies exist on elastic–plastic simulations of truncated contact ellipses. Therefore, a numerical study concerning the contact of a rigid ball with an elastic–plastic plane is presented. Due to an undercut in the plane, a quarter of the theoretical Hertzian contact ellipse is cut off. The aim of the study is to investigate the influence of the undercut angle on the pressure distribution and the elastic and plastic deformation at the edge. The use of FEM shows that the undercut angle has a significant effect on the characteristics of the contact. The results obtained using FEM are then used as a reference for comparison with a semi-analytical method (SAM). It is shown that the SAM, based on the half-space, provides comparable results only for very small undercut angles. Full article
(This article belongs to the Special Issue Numerical Simulations in Lubrication)
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12 pages, 8259 KiB  
Article
A New Finite Element Analysis Model to Estimate Contact Stress in Ball Screw
by Geon-Ho Shin and Jang-Wook Hur
Appl. Sci. 2022, 12(9), 4713; https://doi.org/10.3390/app12094713 - 7 May 2022
Cited by 5 | Viewed by 3974
Abstract
A ball screw is a mechanical part that converts rotational motion into translational motion, but when it receives an excessive axial load, permanent deformation occurs inside. As ball screws are mostly used for precise driving, permanent deformation has a fatal effect on the [...] Read more.
A ball screw is a mechanical part that converts rotational motion into translational motion, but when it receives an excessive axial load, permanent deformation occurs inside. As ball screws are mostly used for precise driving, permanent deformation has a fatal effect on the operation of the system. As this permanent deformation mostly occurs on the contact surface between the ball and other parts, it is necessary to observe the change of internal stress caused by the contact of the parts in order to determine whether permanent deformation occurs. Theoretical calculations or finite element analysis (FEA) are mainly used for the analysis of rotating parts, but existing methods have difficulty in observing stress changes occurring on the narrow contact surface of ball screws. In this paper, a new FEA model that can efficiently estimate the stress caused by internal contact inside the ball screw is presented. This model is a synthetic model that applies theoretical calculation results to a 3D FEA model. Factors derived by theoretical calculation include the shape of the contact surface where the ball and other parts meet and the contact pressure at the contact surface, which were derived by a method based on Hertz contact theory. As a result of observing the internal stress distribution of the ball screw estimated by the model, it was confirmed that the shape was similar to that of the actual stress distribution and, compared with the analysis results of other conventional methods conducted with the same mesh shape, the results of the model presented in this paper were more valid. Full article
(This article belongs to the Special Issue Structural Design and Computational Methods)
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